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Difficulty: MediumMulti-Statement Boolean Evaluation

The table below presents monthly operational and climate metrics for seven commercial cold-storage logistics facilities operated by a regional food distributor during 2025:

Facility CodeStorage Volume (1000 m31000\text{ m}^3)Energy Consumed (MWh/month\text{MWh/month})Avg Storage Temp (∘C^\circ\text{C})Capacity UtilizationOperating Cost ($1000/month\$1000/\text{month})
F-1120480-2285%144
F-2200700-1892%210
F-3150525-2578%175
F-490390-2095%120
F-5250875-2280%260
F-6180630-2488%198
F-73001050-1975%315

True or False: Among the facilities maintaining an average storage temperature colder than −20∘C-20^\circ\text{C}, the median monthly operating cost is greater than $180,000\$180,000.

Answer: Answer

Answer

True
The statement is True because the four facilities with average storage temperatures strictly below −20∘C-20^\circ\text{C} (F-1, F-3, F-5, and F-6) have monthly operating costs of $144,000\$144,000, $175,000\$175,000, $198,000\$198,000, and $260,000\$260,000. The median of these four values is 175+1982×1000=$186,500\frac{175 + 198}{2} \times 1000 = \$186,500, which is strictly greater than $180,000\$180,000.

Step-by-Step Solution

1
Filter the facilities based on the specified temperature condition.
Identified facilities F-1 (−22∘C-22^\circ\text{C}), F-3 (−25∘C-25^\circ\text{C}), F-5 (−22∘C-22^\circ\text{C}), and F-6 (−24∘C-24^\circ\text{C}). Facility F-4 (−20∘C-20^\circ\text{C}) is excluded because −20∘C-20^\circ\text{C} is not strictly colder than −20∘C-20^\circ\text{C}.
The criterion requires temperatures strictly below −20∘C-20^\circ\text{C}.
2
Extract and order the monthly operating costs (in thousands of dollars) for the filtered subset.
Ordered values: 144,175,198,260144, 175, 198, 260.
Sorting values in ascending order is necessary to calculate the median.
3
Calculate the median of the four operating cost values.
Median=175+1982=186.5\text{Median} = \frac{175 + 198}{2} = 186.5 thousand dollars, which equals $186,500\$186,500.
For an even number of observations (n=4n = 4), the median is the mean of the 2nd and 3rd ordered values.
4
Compare the calculated median to the threshold value in the statement.
$186,500>$180,000\$186,500 > \$180,000, confirming the statement is True.
The median operating cost exceeds the threshold of $180,000\$180,000.

Key Concept

Conditional Table Filtering and Median Calculation
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Topics

Multi-Statement Boolean Evaluation

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